Systematic study of favored α-decay half-lives of closed shell odd-A and doubly-odd nuclei related to ground and isomeric states

Abstract

In this work, we systematically investigate the favored $\hat{I}\pm$-decay half-lives and $\hat{I}\pm$ preformation probabilities of both odd-$A$ and doubly-odd nuclei related to ground and isomeric states around the doubly magic cores at $Z=82$, $N=82$ and at $Z=82$, $N=126$, respectively, within a two-potential approach from the view of the valence nucleon (or hole). The results show that the $\hat{I}\pm$ preformation probability is linear related to $N_{\text{p}}{N}_{\text{n}}$ or $N_{\text{p}}{N}_{\text{n}}I$, where $N_{\text{p}}$, $N_{\text{n}}$, and $I$ are the number of valence protons (or holes), the number of valence neutrons (or holes), and the isospin of the parent nucleus, respectively. Fitting the $\hat{I}\pm$ preformation probabilities data extracted from the differences between experimental data and calculated half-lives without a shell correction, we give two analytic formulas of the $\hat{I}\pm$ preformation probabilities and the values of corresponding parameters. Using those formulas and the parameters, we calculate the $\hat{I}\pm$-decay half-lives for those nuclei. The calculated results can well reproduce the experimental data.

9 pages, 6 figures